Open Access Method Article

New Variable Neighborhood Search Structure for Travelling Salesman Problems

A. Hande Erol Bingüler, Serol Bulkan

Journal of Advances in Mathematics and Computer Science, Page 422-434
DOI: 10.9734/BJMCS/2015/14453

In the traveling salesman problem, there are a collection of cities and travel cost between each pair of them. The aim is to find the minimum cost way of visiting all cities and returning to the starting point. This kind of problem is deceptive and one of the most intensely studied problems in computational mathematics. No effective solution method is known for the general case. Variable Neighborhood Search (VNS) is a recent metaheuristic for solving combinatorial and global optimization problems whose basic idea is systematic change of neighborhood within a local search. Its development has been rapid, with several dozen papers already published or to appear. Many extensions have been made, mainly to allow solution of large problem instances. In most of them, an effort has been made to keep the simplicity of the basic scheme. In this study, variable neighborhood search structure as a metaheuristic optimization technique and neighborhood approximation is developed. K-opt neighborhood structure is generated. This new structure’s solvability in benchmark and symmetric traveling salesman problem instances is tested, and results are listed.

Open Access Original Research Article

Linear Mixed Model in the Light of Future Data

Kunio Takezawa

Journal of Advances in Mathematics and Computer Science, Page 370-380
DOI: 10.9734/BJMCS/2015/15514

The maximum likelihood and restricted (or residual) likelihood methods are common tools for estimating variances in linear mixed models. However, regression in the light of future data can yield different results. Investigations into the characteristics of this new variance are expected to promote the effective use of data in fields such as ecology and genetic statistics. Our numerical simulations show that the estimates of variances in the light of future data are substantially different from those given by the maximum likelihood and restricted (or residual) likelihood methods.

Open Access Original Research Article

Diabetes Diagnosis with Maximum Covariance Weighted Resilience Back Propagation Procedure

Olabode Olatubosun, Fasoranbaku Olusoga, Fagbuwagun Abayomi

Journal of Advances in Mathematics and Computer Science, Page 381-393
DOI: 10.9734/BJMCS/2015/14871

This study presents Diabetes Diagnosis with Maximum Covariance Weighted Resilience Back Propagation Procedure. The Maximum covariance method is divided into three phases. A large number of candidate’s hidden units is considered by initializing their various weights with random values. Then the desired number of hidden units is selected amongst the candidates by using the maximum covariance. The weights feeding the output units are calculated with linear regression method. After the maximum covariance initialization, the network is trained with the resilient back propagation which is an adaptive training algorithm. The activation function in the hidden units is hyperbolic tangent function. Ten baseline variables includes, age, sex, body mass index, average blood pressure and six blood serum measurements, were obtained for each of n = 442 diabetes patients, as well as the response of interest, a quantitative measure of disease progression one year after baseline was used. The learning machine was trained, validated and tested. The result shows the algorithm is efficient in the diagnosis of who is a diabetic patient.

Open Access Original Research Article

Forecasting the Number of Muslim Pilgrims Using NARX Neural Networks with a Comparison Study with Other Modern Methods

Esam A. Khan, Mahmoud A. Elgamal, Sameer M. Shaarawy

Journal of Advances in Mathematics and Computer Science, Page 394-401
DOI: 10.9734/BJMCS/2015/14563

Pilgrimage (Hajj) of Muslims is considered the largest human gathering all over the world in which more than three millions move together through a very limited space in a short time period. The yearly number of pilgrims coming from outside Saudi Arabia, denoted by NPO for short, is more than two thirds of the total number of Pilgrims. Therefore forecasting the NPO is considered by Saudi Arabia as the most important indicator in determining the planning mechanism for future secure and comfortable hajj seasons. The main objective of this article is to employ the NARX neural networks to forecast the yearly series of NPO and to show that it gives better forecasts than Box–Jenkins and Bayesian Procedures. In order to achieve our objective, the NARX is used to forecast the future five observations and the results are compared with the results given in [1].

Open Access Original Research Article

Optimal Portfolio for N-Risky and N-Riskless Irreversible Investments

B. A. Salami, C. R. Nwozo

Journal of Advances in Mathematics and Computer Science, Page 402-421
DOI: 10.9734/BJMCS/2015/14583

When a firm decides to make irreversible investment expenditure, it neglects its right without obligation to invest but wait for new desirable information that might affect investment decision. Studies have shown irreversible investments with the underlying value process driven by stochastic differential equations. However, this study had no consideration for a portfolio of N-risky and Nriskless investments (N = 2; 3; ; T < ∞) in relation to the set of: Variable Production Costs (VPC), Periodic Loan Repayment (PLR) with penalty for default, Investment Reserve (IR) and Equipment Value (EV) equations. This study was designed to consider a portfolio of N-risky and N-riskless investments including a set of processes describing VPC for the portfolio, interval PLR for the same investments with penalty processes for default in PLR. A set of instantaneous Expected Revenue (ER) from the risky investments were formulated using Geometric Brownian Motion (GBM) with drift term restricted to zero and volatility strictly positive (Martingale condition). The resulting equation was solved using Ito’s formula. The IR and EV equations were formulated with predictive adaptive processes to examine liquidity of business plan and Equipment Depreciation (ED) value respectively. Maintenance Process (MP) was introduced into the EV equation. The equation describing portfolio option value was formulated using Bellman utility function and solved. Risks associated with the risky investments were measured using Arrow-Pratt measure. Linear Dynamic Optimization (LDO) was adopted to maximise the value of the N-risky and Nriskless investments; and also used for Capital Equipment (CE) value equation with MP to examine depreciation values. Application of this model to a Nigeria maritime industry showed that the set of ER obtained were fluctuating and met the Martingale condition. The equations obtained for the N-Risky and N-Riskless investments gave values as VPC ≅ #29:2M/month, PLR ≅ $37:9M/monthIR = #234:4M; ED ∈ 2 (0.3, 0.4). A set of threshold values for the N-irreversible investments were obtained. The equations obtained from Arrow Pratt yielded 18 to 20% as investors’ attitude towards risk management.

Open Access Original Research Article

Software Design Concerns Associated with Simulating Multiple Inheritance in Java for Implementation Purposes

Fawzi Albalooshi

Journal of Advances in Mathematics and Computer Science, Page 435-443
DOI: 10.9734/BJMCS/2015/15476

OO software development has become the dominant development approach with Java as the common implementation language. A well-known drawback in Java is its limitation in implementing multiple inheritance which is considered by many researchers a fundamental concept in OO. Approaches in simulating multiple inheritance in Java have been thought of and implemented. In this paper some of these approaches are presented and their negative side effects on the developed software are highlighted. The paper addresses important aspects related to implementing multiple inheritance in Java that may be neglected by developers, and proposes two additional steps in the development life cycle when implementing a system with multiple inheritance relationship(s) in Java. This proposed solution as illustrated with examples ensures proper software development practice throughout the development stages even if there are specific requirements to implement multiple inheritance in Java.

Open Access Original Research Article

On the Construction of Odd Length Quantum Codes

Manish Gupta, R. K. Narula, Divya Taneja

Journal of Advances in Mathematics and Computer Science, Page 444-450
DOI: 10.9734/BJMCS/2015/15059

In this paper, we endeavor for an extensive study of [[n,n-3,2]] codes of odd length. We begin with the computation of the linear programming bound on the dimension of distance 2 codes of odd length and show that the [[n,n-3,2]] codes are optimal. We next find their generator matrix, stabilizer structure and also show that these codes are impure or degenerate except the [[3,0,2]] code which is pure by convention. In degenerate codes, distinct errors do not necessarily take the code space to orthogonal space. So sometimes they can correct more errors than that they can identify and has the capacity to store more information than a nondegenerate code. The present paper also establishes the existence of ((2m+1,2^(2m-2),2)) codes from the ((2m,2^(2m-2),2)) codes for all m>1. We have also constructed another class of distance 2 codes which are constructed using distance 3 codes.